In order to study the transfer of water borne 1 J , Cs and *°Sr into rice plants, pot experiments were done by growing rice plants on soils taken from rice beds near two nuclear power plants: Qinshan Nuclear Power Plant and Daya Bay Nuclear Power Plant in China. The vertical migration of '"Cs and ''Sr in the soil samples due to leaching was studied, and results show that almost all the contamin...

LetGn,r(K) be the Grassmannian manifold of k-dimensionalK-subspaces in K where K = R,C,H is the field of real, complex or quaternionic numbers. We consider the Radon, cosine and sine transforms, Rr′,r, Cr′,r and Sr′,r, from the L space L2(Gn,r(K)) to the space L 2(Gn,r′(K)), for r, r ′ ≤ n − 1. The L spaces are decomposed into irreducible representations of G with multiplicity free. We compute ...

We study some properties of positive solutions to the higher order conformally invariant equation with a singular set $$\begin{aligned} (-\Delta )^m u = u^{\frac{n+2m}{n-2m}} ~~~~~~ \text {in} ~ \Omega \backslash \Lambda , \end{aligned}$$ where $$\Omega \subset {\mathbb {R}}^n$$ is an open domain, $$\Lambda $$ closed subset $${\mathbb $$1 \le m < n/2$$ and integer. first establish local estimat...

We have measured the density of negative surface charges near the voltage sensor for inactivation gating of (L-type) Ca channels in intact calf Purkinje fibers and in isolated myocytes from guinea pig and rat ventricles. Divalent cation-induced changes in the half-maximal voltage for inactivation were determined and were well described by curves predicted by surface potential theory. We measure...

Let X and Y be Banach spaces, G an open subset of X. If we denote the closure of G by cl(G), let ƒ be a mapping of cl(G) into Y. For X~ Y and ƒ a compact mapping, Leray and Schauder [9] gave a definition of topological degree for mappings of the form ƒ —ƒ on the open set G over a point a of X whenever (I—f)"^) is a compact subset of G. The Leray-Schauder degree for compact displacements is the ...

the known theory for an oid t shows how to find a subset t of ?t, which is a compact right topological semigroup [i]. the success of the methods in [2] for obtaining properties of-t has prompted us to see how successful they would be in another context. thus we find (theorem 4.8) that t cont ains copies of free semigroups on 2? generators, is an immediate consequence of the stronger result and ...

In a compact geodesic metric space of topological dimension one, the minimal length of a loop in a free homotopy class is well-defined, and provides a function l : π1(X) −→ R+ ∪ ∞ (the value ∞ being assigned to loops which are not freely homotopic to any rectifiable loops). This function is the marked length spectrum. We introduce a subset Conv(X), which is the union of all non-constant minimal...

— We introduce the notion of k-self-similarity for compact subsets of R and show that it is a natural analogue of the notion of k-automatic subsets of integers. We show that various wellknown fractals such as the triadic Cantor set, the Sierpiński carpet or the Menger sponge, turn out to be k-self-similar for some integers k. We then prove an analogue of Cobham’s theorem for compact sets of R t...

Hofmann and Morris [6] proved that a locally compact connected group G has a finite subset generating a dense subgroup if and only if the weight w(G) of G does not exceed c , the cardinality of the continuum. The minimum cardinality of such a topological generating set is an invariant of the group, is denoted by σ(G), and is called the topological rank of G . For compact abelian groups of weigh...

The -pseudospectrum of a matrix A is the subset of the complex plane consisting of all eigenvalues of complex matrices within a distance of A, measured by the operator 2-norm. Given a nonderogatory matrix A0, for small > 0, we show that the -pseudospectrum of any matrix A near A0 consists of compact convex neighborhoods of the eigenvalues of A0. Furthermore, the dependence of each of these neig...